If a quadratic form $f(x,y)=ax^2+bxy+cy^{2}$ is defined over a polynomial ring $R(t)$, R is a commutative ring with unity, then, how does a uni modular transformation is defined? Also, what is the matrix associated with this?

Do I get any references on this

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    $\begingroup$ Over a finite field, or over a polynomial ring? How are you defining a quadratic form over a polynomial ring, $a$, $b$, and $c$ are polynomials? $\endgroup$ – Morgan Rodgers Dec 20 '17 at 7:10
  • $\begingroup$ I edited the question. $\endgroup$ – thanks Dec 20 '17 at 7:14

The polynomial ring $R[t]$ (not $R(t)$) is, among other things, a commutative ring with unity.

So, the definitions for quadratic forms over commutative rings with unity apply.

  • $\begingroup$ Hurkyl, do I get any material on this $\endgroup$ – thanks Dec 20 '17 at 7:24

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